Question

△jkl ~ △fgh. find the values of x and y.

Explanation:

Step1: Find the scale factor

Since $\triangle{JKL}\sim\triangle{FGH}$, the ratio of corresponding sides is the same. The ratio of the side lengths of $\triangle{JKL}$ to $\triangle{FGH}$ for the pair of known corresponding sides is $\frac{20}{15}=\frac{4}{3}$.

Step2: Find the value of $x$

Side $KL = 12$ corresponds to side $HG=x$. Using the scale - factor, we have $\frac{12}{x}=\frac{4}{3}$. Cross - multiply: $4x = 12\times3$, so $4x=36$, and $x = 9$.

Step3: Find the value of $y$

Side $JL = 16$ corresponds to side $FG = y$. Using the scale - factor $\frac{16}{y}=\frac{4}{3}$. Cross - multiply: $4y=16\times3$, so $4y = 48$, and $y = 12$.

Answer:

$x = 9$, $y = 12$